INVARIANCE OF CLOSED CONVEX-SETS AND DOMINATION CRITERIA FOR SEMIGROUPS

Let a and b be two positive continuous and closed sesquilinear forms o n the Hilbert space H = L(2)(Omega, mu). Denote by T = T(t)(t greater than or equal to 0) and S = S(t)(t greater than or equal to 0), the se migroups generated by a and b on H. We give criteria in terms of a and b guaranteeing that the semigroup T is dominated by S, i.e. \T(t)f\ l ess than or equal to S(t)\f\ for all t greater than or equal to 0 and f is an element of H. The method proposed uses ideas on invariance of closed convex sets of H under semigroups. Applications to elliptic ope rators and concrete examples are given.